An ice sculpture in the form of a sphere melts in such a way that it maintains its spherical shape. The volume of the sphere is decreasing at a constant rate of 2r cubic meters per hour. At what rate, in square meters per hour, is the surface area of the sphere decreasing at the moment when the radius is 5 meters? (Note: For a sphere of radius r, the surface area is 4r² and the volume is 4Tr.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
An ice sculpture in the form of a sphere melts in such a way that it maintains its spherical
shape. The volume of the sphere is decreasing at a constant rate of 2n cubic meters per hour. At
what rate, in square meters per hour, is the surface area of the sphere decreasing at the moment
when the radius is 5 meters? (Note: For a sphere of radius r, the surface area is 4ar and the
volume is 4r.)
Transcribed Image Text:An ice sculpture in the form of a sphere melts in such a way that it maintains its spherical shape. The volume of the sphere is decreasing at a constant rate of 2n cubic meters per hour. At what rate, in square meters per hour, is the surface area of the sphere decreasing at the moment when the radius is 5 meters? (Note: For a sphere of radius r, the surface area is 4ar and the volume is 4r.)
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